A hybrid vehicle on which an engine (internal combustion engine), a motor (generator motor) for driving and regenerating and a battery (electricity storage reservoir) has been known. In the hybrid vehicle, which the motor starts up the engine, start-up torque of the motor has been determined based on the engine temperature (cooling water temperature) conventionally. Such conventional engine start-up control as this has the problem that a battery deterioration is likely to be hastened due to a heavy load caused by excessive current extraction when electricity is supplied to the motor from the battery for starting up the engine while it is cool. In connection with this problem Japan Laid-Open Patent 11-153075 discloses a technique (start-up control apparatus for an internal combustion engine) which restrains an excessive load from acting on a battery by controlling the output torque of a motor to be smaller as the engine temperature falls.
However, the start-up control apparatus fails in starting up an engine due to unnecessary output restriction or causes reduction in the quality of the engine exhaust gas emissions even if engine start-up is successful, when an engine temperature is low while a battery temperature is not low. On the other hand, when the engine temperature is high while the battery temperature is low, acceleration of battery deterioration occurs since undesired excessive electricity is extracted from the battery without appropriate output restriction.